A random sample of 5200 permanent dwellings on an entire reservation showed that

Question

A random sample of 5200 permanent dwellings on an entire reservation showed that 1550 were traditional hogans.

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. A random sample of 5200 permanent dwellings on an entire reservation showed that 1550 were traditional hogans. (a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.) 2981 (b) Find a 99% confidence interval for p. (Round your answer to three decimal places.) lower limit upper limit Give a brief interpretation of the confidence interval. O 99% of the confidence intervals created using this method would include the true proportion of traditional hogans. 1% of the confidence intervals created using this method would include the true proportion of traditional hogans. 1% of all confidence intervals would include the true proportion of traditional hogans. 99% of all confidence intervals would include the true proportion of traditional hogans. (c) Do you think that np 5 and ng 5 are satisfied for this problem? Explain why this would be an important consideration. Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately binomial. O No, the conditions are not satisfied. This is important because it allows us to say that p is approximately normal. o Yes, the conditions are satisfied. This is important because it allows us to say that p is approximately normal. O No, the conditions are not satisfied. This is important because it allows us to say that bis approximately binomial.

Explanation / Answer

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
No. of success(x)=1550
Sample Size(n)=5200
Sample proportion = x/n =0.2981
Confidence Interval = [ 0.2981 ±Z a/2 ( Sqrt ( 0.2981*0.7019) /5200)]
= [ 0.2981 - 2.576* Sqrt(0) , 0.2981 + 2.58* Sqrt(0) ]
= [ 0.282,0.315]

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